The woman that led police on a high speed pursuit through the streets of Sydney told court she was 'full of anxiety' during the chase.

Sally Arabi, 23, has been named as the woman who allegedly reached speeds of up to 150km/h as she sped through the streets of Cabramatta in south west Sydney on Thursday night, according to Seven News.

Police allege Ms Arabi ran two red lights that triggered a chase after she did not pull over for officers at 10.30pm.

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Sally Arabi (pictured) was allegedly involved in a high speed car pursuit with police

CCTV footage captured Sally Arabi driving through the streets of south west Sydney

Security cameras captured parts of the chase, which lead onto the Hume Highway before hitting a shocking 150km/h through Rookwood Road at Yagoona.

When police eventually pulled the 23-year-old over in Birrong, after entering the Hume Highway, they were shocked to find a three-year-old toddler in the car and her boyfriend.

'Any sort of reckless behaviour and especially evading police, but having a child in the car is just disgraceful,' Assistant Commissioner Michael Corboy said.

Ms Arabi appeared in court, apologising for her behaviour, on Friday where she was granted bail and will return next month.

No one was hurt in the high speed chase.

Sally Arabi (pictured left) with her boyfriend (pictured right)

Sally Arabi, 23, in hoodie leaving court after she apologised to the magistrate